Information on Result #686284

Linear OA(8172, 2097176, F8, 28) (dual of [2097176, 2097004, 29]-code), using construction X applied to Ce(27) ⊂ Ce(24) based on
  1. linear OA(8169, 2097152, F8, 28) (dual of [2097152, 2096983, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
  2. linear OA(8148, 2097152, F8, 25) (dual of [2097152, 2097004, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(83, 24, F8, 2) (dual of [24, 21, 3]-code), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(8173, 2097177, F8, 28) (dual of [2097177, 2097004, 29]-code) [i]Code Embedding in Larger Space
2Linear OOA(8172, 1311424, F8, 2, 28) (dual of [(1311424, 2), 2622676, 29]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(8172, 1311424, F8, 3, 28) (dual of [(1311424, 3), 3934100, 29]-NRT-code) [i]
4Digital (144, 172, 1311424)-net over F8 [i]
5Linear OOA(8172, 1048588, F8, 2, 28) (dual of [(1048588, 2), 2097004, 29]-NRT-code) [i]OOA Folding
6Linear OOA(8172, 699058, F8, 3, 28) (dual of [(699058, 3), 2097002, 29]-NRT-code) [i]
7Linear OOA(8172, 149798, F8, 28, 28) (dual of [(149798, 28), 4194172, 29]-NRT-code) [i]OA Folding and Stacking